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In this MO question, user Martin Brandenburg asks about God's number for $n \times n \times n$-cubes for $n>3$. Here, God's number $g(n)$ was defined as the smallest number $m$ such that every realizable arrangement of the $n \times n \times n$-cube can be solved within $m$ moves.

We could generalize the notion of God's number to $n^{k}$-dimensional cubes, where $k >3$. Define $g_{k}(n)$ as the smallest number $l$ such that every realizable arrangement of the $n^{k}$-cube can be solved within $l$ moves.

Whereas Mr. Brandenburg's question pertains to three dimensional Rubik's cubes ($k=3$), I wonder what is known about higher God's number for higher dimensional sequential move puzzles.

Questions:

1. Is $g_{4}(2)$ known? And what about $g_{4}(3)$?
2. What is known about the asymptotic value of $g_{k}(n)$?

In this MO question, user Martin Brandenburg asks about God's number for $n \times n \times n$-cubes for $n>3$. Here, God's number $g(n)$ was defined as the smallest number $m$ such that every realizable arrangement of the $n \times n \times n$-cube can be solved within $m$ moves.

We could generalize the notion of God's number to $n^{k}$-cubes, where $k >3$ is the number of dimensions. Define $g_{k}(n)$ as the smallest number $l$ such that every realizable arrangement of the $n^{k}$-cube can be solved within $l$ moves.

Whereas Mr. Brandenburg's question pertains to three dimensional Rubik's cubes ($k=3$), I wonder what is known about higher God's number for higher dimensional sequential move puzzles.

Questions:

1. Is $g_{4}(2)$ known? And what about $g_{4}(3)$?
2. What is known about the asymptotic value of $g_{k}(n)$?

In this MO question, user Martin Brandenburg asks about God's number for $n \times n \times n$-cubes for $n>3$. Here, God's number $g(n)$ was defined as the smallest number $m$ such that every realizable arrangement of the $n \times n \times n$-cube can be solved within $m$ moves.

We could generalize the notion of God's number to $n^{k}$-dimensional cubes, where $k >3$. Define $g_{k}(n)$ as the smalles number $l$ such that every realizable arrangement of the $n^{k}$-cube can be solved within $l$ moves.

Whereas Mr. Brandenburg's question pertains to three dimensional Rubik's cubes ($k=3$), I wonder what is known about higher God's number for higher dimensional sequential move puzzles.

Questions:

1. Is $g_{4}(2)$ known? And what about $g_{4}(3)$?
2. What is known about the asymptotic value of $g_{k}(n)$?

In this MO question, user Martin Brandenburg asks about God's number for $n \times n \times n$-cubes for $n>3$. Here, God's number $g(n)$ was defined as the smallest number $m$ such that every realizable arrangement of the $n \times n \times n$-cube can be solved within $m$ moves.

We could generalize the notion of God's number to $n^{k}$-dimensional cubes, where $k >3$. Define $g_{k}(n)$ as the smallest number $l$ such that every realizable arrangement of the $n^{k}$-cube can be solved within $l$ moves.

Whereas Mr. Brandenburg's question pertains to three dimensional Rubik's cubes ($k=3$), I wonder what is known about higher God's number for higher dimensional sequential move puzzles.

Questions:

1. Is $g_{4}(2)$ known? And what about $g_{4}(3)$?
2. What is known about the asymptotic value of $g_{k}(n)$?

In this MO question, user Martin Brandenburg asks about God's number for $n \times n \times n$-cubes for $n>3$.

  Here, God's number $g(n)$ was defined as the smallest number $m$ such that every realizable arrangement of the $n \times n \times n$-cube can be solved within $m$ moves. We could generalize the notion of God's number to $n^{k}$-dimensional cubes, where $k >3$. Define $g_{k}(n)$ as the smalles number $l$ such that every realizable arrangement of the $n^{k}$-cube can be solved within $l$ moves.

Whereas Mr. Brandenburg's question pertains to three dimensional Rubik's cubes ($k=3$), I wonder what is known about higher God's number for higher dimensional sequential move puzzles.

Questions:

1. Is $g_{4}(2)$ known? And what about $g_{4}(3)$?
2. What is known about the asymptotic value of $g_{k}(n)$?

In this MO question, user Martin Brandenburg asks about God's number for $n \times n \times n$-cubes for $n>3$. Here, God's number $g(n)$ was defined as the smallest number $m$ such that every realizable arrangement of the $n \times n \times n$-cube can be solved within $m$ moves. 

We could generalize the notion of God's number to $n^{k}$-dimensional cubes, where $k >3$. Define $g_{k}(n)$ as the smalles number $l$ such that every realizable arrangement of the $n^{k}$-cube can be solved within $l$ moves.

Whereas Mr. Brandenburg's question pertains to three dimensional Rubik's cubes ($k=3$), I wonder what is known about higher God's number for higher dimensional sequential move puzzles.

Questions:

1. Is $g_{4}(2)$ known? And what about $g_{4}(3)$?
2. What is known about the asymptotic value of $g_{k}(n)$?